The Hamiltonian \(H\)  in Eq. (REF ) is gauge dependent and singular. To compare different
approaches one has to either relate the Hamiltonians by canonical transformations or to compare the predictions for
the resulting observables. This applies to the case of harmonic coordinates in the present approach and
effective one body coordinates in [1]}. In Ref. [1]} different methods
and constraints implied by the \(\nu \) -structure of the expansion coefficients of the scattering angle \(\chi _k\) ,
(REF ), have been used to construct the
Hamiltonian and all but two \(O(\nu ^2)\)  parameters, \(\bar{d}_5\)  and \(a_6\) , were determined
in this way for \(H_{\rm EOB}\)  up to 5PN.
